Epicycle Studio
Turn a picture into a sketch, draw it with spinning circles, and get its equation.
- Outline editor with smart edges, down to 1 px
- Every layer drawn at once: circles, gears, cranes or polygons
- Poster, equation and MP4 video export
Orrery
A small suite of tools for shapes, math and data. Each tool works on its own, and they pass work to each other: use Send to in the top bar, or Open file to drop in a photo or a saved Orrery file.
JSON Atlas
Open any JSON, however large, as a graph or tree. Coefficient files redraw their shape.
- Shape view rebuilds and checks Epicycle exports
- Graph and Tree views with no size limit
- Search, path copy, PNG and SVG export
Pochoir
Analyse an image's colors and turn it into stencil layers, ready to print, cut and spray.
- Color analysis: dominant colors, contrast, warmth, suggested layer count
- 1 to 8 stencils by tone or color, with automatic bridges
- DTF transfers for t-shirts, hoodies, caps and mugs
← Part of the Bourzik lab · 3 tools · version 0.0.3 Beta · About and what's new
About Orrery
v0.0.3 BetaOrrery is a small suite of tools for shapes, maths and making things. Each tool works on its own, and they pass work to each other.
Orrery is part of the Bourzik lab of small, free browser tools.
The name comes from the orrery, a clockwork model of the solar system in which gears turn arms and small planets circle on the ends of those arms: circles riding on circles. That is exactly how Epicycle Studio draws a shape, and the suite grew out of it.
The tools
Epicycle Studio
Epicycle Studio turns a picture into an outline, then redraws that outline with chains of spinning arms, the same "circles on circles" astronomers once used for the planets. Fourier showed that any closed shape can be built this way, and the app gives you the exact recipe as an equation.
- Upload a photo and loosely circle the part you want. The app finds the edges; fix tricky spots with the Keep and Remove brushes and the edge buffer.
- The outline becomes a sketch of straight lines you can reshape by dragging points.
- Watch it being drawn as circles are added, from 1 up to 300. Several layers can be drawn at once, each with its own pair of chains, shown as circles, gears, cranes or polygons.
- Save a poster, copy the equation for Desmos, GeoGebra or LaTeX, record a video, or send the design to Pochoir to make stencils.
Good for: math lessons, logos and portraits drawn by circles, social videos, starting points for stencils.
JSON Atlas
JSON Atlas opens any JSON file, however large, as a map of cards or as a tree you can scroll. When the file holds Fourier coefficients, such as an Epicycle Studio export, it redraws the shape from the numbers alone and checks them.
- Paste JSON, open a file, or receive one from another tool.
- Move around the graph, open and close branches, or switch to the tree. Search finds any key or value.
- Export the view as PNG or SVG, or send a shape on to Epicycle Studio or Pochoir.
Good for: checking exports, exploring API data, explaining data structures.
Pochoir
Pochoir reads the colours of an image and splits it into stencil layers, one per paint colour, ready to print, cut and spray. It can also make a colour poster, or a full-colour DTF transfer file for t-shirts, hoodies, caps and mugs.
- Upload a photo, or a design from Epicycle Studio (each layer becomes one stencil).
- Choose how many layers, how they split (by tone or colour), how easy the shapes are to cut, and a colour style.
- Print the stencils as a real-size PDF with clear cut and keep areas, save the colour sheet, or export a poster.
- For DTF, pick the product and placement: you get a transparent 300 DPI PNG at the right size, optional gang sheet, and a placement guide.
Good for: street-art stencils, screen-print separations, pop-art posters, custom apparel and drinkware.
Working together
- Send to in the top bar lists every tool that can take what you made, and opens it there.
- Open file takes a photo or a saved Orrery file and opens it in the right tool.
- The back arrow returns to the tool you came from.
| From | Gives | Goes to |
|---|---|---|
| Epicycle Studio | the design, the equation, the traced photo | Pochoir, JSON Atlas |
| JSON Atlas | an equation or design found in the JSON | Epicycle Studio, Pochoir |
| Pochoir | the stencil result, the colour sheet | Epicycle Studio, JSON Atlas |
Your files stay with you
Everything runs in your browser. Photos and designs are never uploaded; files are only saved when you choose to save them.
Open-source libraries, loaded only when needed: jsPDF and JSZip (PDF and ZIP files), color-name-list (colour names), Delaunator (low-poly facets) and mp4-muxer (video), all MIT or ISC licensed.
Versions
Bump for a significant new feature (0.0.x) or a huge update (0.x.0). Small fixes and visual touch-ups do not change the version. Newest release first.
v0.0.3 Beta2026-10-18 · 60-second and 4K videos
- Epicycle Studio videos: up to 60 seconds, with more laps in longer videos so the build-up keeps its pace.
- Epicycle Studio videos: 4K (2160 × 2160 square, 2160 × 3840 story, 3840 × 2160 wide) and 60 fps, with higher bitrates tuned for quality.
- Encoding picks H.264, then HEVC, VP9 or AV1 at the level the size needs, and writes the file in disk-backed pieces so long 4K videos do not have to fit in memory; the dialog shows the size and time left.
v0.0.2 Beta2026-10-18 · Live log, forged equation and colour themes in videos
- Epicycle Studio videos: a live log panel scrolls during the drawing, one line per step, with each lap, the circles added per layer (radius r and angle φ) and the error dropping lap by lap.
- Epicycle Studio videos: the finale forges the equation letter by letter, white-hot with sparks, cooling to colour 1 for x(t) and colour 2 for y(t); the shape moves aside, to the right in wide videos.
- Epicycle Studio videos: colour themes Ember, Morocco (red, olive green and gold edges), Lagoon, Citrus and Mono, or your own background, two colours and edge colour.
- Orrery: a Back to Bourzik link in the top bar, the home screen and the About page.
v0.0.1 Beta2026-10-18 · First public beta
- Suite: one top bar on every tool with Back, Home, tool tabs, Open file and Send to; tools pass photos, designs, equations and JSON to each other, with conversion where needed.
- Epicycle Studio: outline editor with lasso, colour-aware Keep and Remove brushes and an edge buffer from 1 to 20 px; sketch editing; Fourier epicycles from 1 to 300 circles; layered designs.
- Epicycle Studio: construction-site mode, one pair of chains per layer, all turning together; arm styles Circles, Gears, Cranes and Polygons.
- Epicycle Studio: poster export as PNG, JPEG or SVG; equation for Desmos, GeoGebra, LaTeX, plain text and JSON, with free online checkers.
- Epicycle Studio: video recorder, MP4 in square, story or wide format, with neon glow, camera pull-back, spectrum ring, circle counter and typed caption.
- JSON Atlas: graph and tree views with no size limit, search, PNG and SVG export; Shape view redraws and checks Fourier coefficients.
- Pochoir: colour analysis, 1 to 8 stencil layers by tone or colour, cutting ease and automatic bridges, faceted low-poly looks, style palettes and a colour sheet.
- Pochoir: print-and-cut vector PDF from A4 to B1 with a cut/keep guide, SVG and ZIP; posters up to cinema sizes.
- Pochoir: DTF transfers for t-shirts, youth wear, hoodies, caps and drinkware, with sizes from common transfer-shop guides; transparent 300 DPI PNG, 22-inch gang sheets and a placement guide PDF.
drawn with Fourier epicycles
–match · error –
x(t)1 circle
y(t)1 circle
Save
Drop the image to trace it
Epicycle Studio image → sketch → equation
?How it works, in plain words▼
Fourier epicycles are a way to draw any closed outline using nothing but spinning circles. Each circle is pinned to the edge of the one before it, like a chain of clock hands of different lengths turning at different speeds. A pen sits at the tip of the last circle, and as everything spins, the pen traces your shape.
Big circles turn slowly and give the rough outline. Small circles turn fast and add the fine details. The more circles you stack, the closer the drawing gets to the real shape.
The idea comes from two places. Ancient astronomers used “circles on circles” (epicycles) to describe how planets move across the sky. In 1807, the mathematician Joseph Fourier showed that any repeating motion can be built by adding up simple rotations. This app puts the two together.
What the app does with your image
- Finds the subject. You loosely circle the shape on your photo, and the app finds its exact edges. You can zoom in and fix any edge it gets wrong.
- Turns it into a sketch. The border becomes straight lines joined by points you can drag to reshape it.
- Measures the circles. It walks around the sketch at an even pace and works out how big each circle must be and where it starts.
- Draws with two chains. The orange chain sets how far left or right the pen is, the purple chain sets how high or low. The pen is where the two dashed lines meet.
- Adds circles each turn. It starts with 1 circle per chain and builds up to 300. The ring in the corner shows how closely the drawing matches your sketch.
- Gives you the recipe. At the end, the arms stop and you get the finished shape with its equation. The equation is the exact list of circles, so anyone can redraw your shape from it.
Reading the equation
- t
- Time. It goes from 0 to 2π, which is one full lap around the shape.
- a₀, c₀
- The center of the shape, where the first circle is pinned.
- k
- Which circle, and how fast it spins: circle k turns k times per lap.
- aₖ, bₖ, cₖ, dₖ
- The size and starting angle of circle k. These are the numbers in the table below.
- N
- How many circles are added together. More circles, smaller error.
01Shape
Upload a photo or drawing, or paste or drop one on the canvas. An editor opens where you can move and zoom the photo, loosely circle the shape you want, and fix tricky edges. The outline then becomes a sketch of straight lines.
0 points in the selected layer. Drag a point to move it, tap a line to add one, double-tap a point to remove it.
Layerspainted first at the top
Add the eyes, the glasses or the hair as their own layers: each layer is drawn by its own circles and gets its own color.
surface color for the stencils
Pochoir turns each layer into one stencil, in this order, ready to print and cut.
02Epicycles
one pair of chains per layer
A build-up adds circles each turn, from 1 to 300 on each arm. When it reaches the most accurate level, the circles stop and the view settles on the finished shape and its equation.
03Equation
x(t) = a0 + NΣk=1 [ ak cos kt + bk sin kt ]
y(t) = c0 + NΣk=1 [ ck cos kt + dk sin kt ]
t ∈ [0, 2π]N = 1error –
ak = (1/π) ∫02π x(t) cos(kt) dt (bk, ck, dk alike)
6 coefficients computed from the sketch
Units are normalized: the shape is centered at the origin, its larger side spans −1 to 1, and y points up.
Check it online, for free
- Desmosgraphing calculator · Desmos format
- GeoGebragraphing calculator · GeoGebra format
- CodeCogsLaTeX equation viewer · LaTeX format
- Wolfram|Alphaquick plot of the first circles, opens ready to run
- JSON Atlasredraws the shape from the JSON and checks it · JSON format
- SVG vieweropen or paste a saved SVG poster
| k | ak | bk | ck | dk |
|---|
Saving files isn’t available in this view. Press and hold the image (or right-click it) to save it.
Record a video
The video follows the arm style and layers chosen in the studio. It is rendered frame by frame, so it is smooth even on a slow device.
Mark your shapeFinding the shape…
100%
Finding the edges…
Ready
Shape
Rebuilt from the numbers in this file, independently of the app that made it.
keystringnumberbooleannull
Path
rootDrop a .json file to open it
Loading…
Tap a colorway to use it
Dominant colors
Measurements
Lightness
Hue wheel
What this means for stencils
Cutting the layers…
Drop the image to analyse it
Saving files isn’t available in this view. Press and hold (or right-click) to save the image.